Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 3, 2014

Detecting extra dimensions by Hydrogen-like atoms

Zhou Wan-Ping, Zhou Peng and Qiao Hao-Xue
From the journal Open Physics

Abstract

We reconsider the idea in spectroscopy of detecting extra dimensions by regarding the nucleus as a homogeneous sphere. In our results, it turns out that the gravitational potential inside the nucleus is much stronger than the potential induced by a particle in the same regime in ref. [16], and thus a more significant correction of the ground state energy of hydrogen-like atoms is obtained, which can be used to determine the existence of ADD’s extra dimensions. In order to get a larger order of magnitude for the correction, it is better to apply our theory to high-Z atoms or muonic atoms, where the volume of the nucleus can’t be ignored and the relativistic effect is important. Our work is based on the Dirac equation in aweak gravity field, and the result is more precise.

References

[1] J. Polchinski, String Theory, Vol. I.II. (Cambridge University Press, Cambridge, England, 1998) 10.1017/CBO9780511618123Search in Google Scholar

[2] C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004) 10.1017/CBO9780511755804Search in Google Scholar

[3] M.K. Parikh, Gen. Rel. Grav. 36, 2419 (2004) 10.1023/B:GERG.0000046850.67053.49Search in Google Scholar

[4] S.W. Hawking, Commun. Math. Phys. 43, 199 (1975) 10.1007/BF02345020Search in Google Scholar

[5] C. Corda, Eur. Phys. J. C 73, 2665 (2013) 10.1140/epjc/s10052-013-2665-6Search in Google Scholar

[6] C. Corda, Int. Journ. Mod. Phys. D 21, 1242023 (2012) 10.1142/S0218271812420230Search in Google Scholar

[7] N.A. Hamed, S. Dimopoulos, G. Dvali, Phys. Lett. B 429, 263 (1998) 10.1016/S0370-2693(98)00466-3Search in Google Scholar

[8] N.A. Hamed, S. Dimopoulos, G. Dvali, Phys. Rev. D 59, 086004 (1999) Search in Google Scholar

[9] N.A. Hamed, S. Dimopoulos, G. Dvali, J.M. Russell, Phys. Rev. D 65, 024032 (2002) Search in Google Scholar

[10] D.J. Kapner et al., Phys. Rev. Lett. 98, 021101 (2007) 10.1103/PhysRevLett.98.021101Search in Google Scholar

[11] V.P. Goncalves, W.K. Sauter, M. Thiel, Phys. Rev. D 89, 076003 (2014) 10.1103/PhysRevD.89.076003Search in Google Scholar

[12] H. Sun, arXiv:1406.3897 Search in Google Scholar

[13] G.F. Giudice, R. Rattazzi, J.D. Wells, Nucl. Phys. B 544, 3 (1999) 10.1016/S0550-3213(99)00044-9Search in Google Scholar

[14] S. Dimopoulos, G. Landsberg, Phys. Rev. Lett. 87, 161602 (2001) 10.1103/PhysRevLett.87.161602Search in Google Scholar

[15] C. Hanhart, J.A. Pons, D.R. Phillips, S. Reddy, Phys. Lett. B. 509, 1 (2001) 10.1016/S0370-2693(01)00544-5Search in Google Scholar

[16] F. Luo, H.Y. Liu, Chin. Phys. Lett. 23, 2903 (2006) 10.1088/0256-307X/23/11/006Search in Google Scholar

[17] F. Luo, H.Y. Liu, Int. J. Theor. Phys. 46, 606 (2007) 10.1007/s10773-006-9164-6Search in Google Scholar

[18] Y.X. Liu, X.H. Zhang, Y.S. Duan, Mod. Phys. Lett. A 23, 1853 (2008) 10.1142/S0217732308026029Search in Google Scholar

[19] A. Zee, Quantum field theory in a nutshell (Princeton University Press, Princeton, 2003) Search in Google Scholar

[20] H.A. Bethe, E.E. Salpeter, Quantum mechanics of one- and twoelectron atoms (Plenum, New York, 1977)10.1007/978-1-4613-4104-8Search in Google Scholar

Received: 2014-3-30
Accepted: 2014-9-8
Published Online: 2014-11-3
Published in Print: 2015-1-1

© 2015 Zhou Wan-Ping et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow